(Adapted from applicant's abstract): The overall goal of this continuing project is to develop efficient algorithms that will permit the development of mathematical models that relate normal and pathological renal function to the underlying membrane transport and flow processes in the renal tubules and their associated vasculature. The primary thrust of this research during the next period will be: To extend our present models at the physiological level to include: (a) Additional architectural features particularly a more detailed representation of the relation of vascular and tubular elements. (b) A more detailed representation of the transmural movement of water and solutes that takes into account both cellular and paracellular pathways. (c) The addition of the solutes H+, HCO3-, HPO4--, H2PO4-, NH4+, CO2, and certain of the organic osmolytes found in the medulla to the Na+, K+, Cl-, and urea already included in the models. (d) The exchange of electrolytes and water between red blood cells and plasma in the vasa recta. (e) A more detailed analysis of time dependent behavior, in particular the transition from diuresis to antidiuresis, and control of the excretion of Na, K, urea, and water by ADH, ANF, and aldosterone, To vectorize the present algorithms in a way that permits the efficient application of the parallel processing capabilities of supercomputer facilities. (a) Improve the stability (and, if necessary, the accuracy) of the numerical methods. (b) Develop hierarchal solution strategies of Multigrid type. (c) Develop general purpose algorithms that will guarantee the convergence of iterative schemes for the solution of model equations by using continuation and smoothing methods. (d) Develop improved methods for estimating the ranges of the significant parameters of the kidney. MINOS - the constrained nonlinear optimization package - will continue to be used on preliminary studies. A complementary aim is to make the non-linear Schur Complement type methods developed by us readily available to other biomedical modelers, and thus, to implement a variety of models on whole kidney and medulla. (b) Models of isolated perfused kidney. (c) Models of epithelia and isolated perfused tubules. (d) A multi-cell model of the macula densa of the cortical ascending limb and its role in the transmission of the tubuloglomerular feedback response. (e) Models for verifying by quantitative simulations hypotheses for mechanisms of neuronal function.